If he says his name is Billy Bob, he should be required to prove it. Like when a shoplifter says "I just bought this" has to produce the receipt.
It is really not possible for the authorities to conduct an independent investigation of all deportees to find out if they are lying about being here illegally. Numerically, it is impossible. For one thing, the authorities would have to prove a negative. They can prove that someone is here legally, but can't prove that someone isn't here illegally. Especially when that person self-identifies as being here illegally. She gave a fake name. Now the authorities are not only obliged to prove she's here illegally, but she's not who she claims to be.
They took this girls word that her name was Selena Gomez and she was apparently a Black Colombian illegal who didn't speak a word of Spanish, why should the authorities question an illegal who says his name is Billy Bob? why should they try to prove the identity of the Hispanic when they didn't even bother with the Black girl? you can't have it both ways, you either identify the people you have in custody or just take their word for everyone across the board.
It's called a statement against interest. It's saying something that a person who didn't commit that act woud not normally say.
A person here legally would not normally lie about their identity giving a name closely associated with a class of persons known to be here illegally. The difference is, someone might lie about their identity to get a benefit but would not lie about their identity to get a detriment when they are entitled to the benefit. The state of the law is, and it's the real state of the law, not what we wish it to be. People to be deported will be asked their names. Whatever name they provide will be accepted as their true name. They will be deported under that name. If they claim to be legal citizens they will be required to produce identification to prove that. They are not asked to produce identification to prove they are here illegally. If they admit to being here illegally, that will not be questioned further.